Stability, energy functionals, and Kahler-Einstein metrics
Stability, energy functionals, and Kahler-Einstein metrics
复制标题
稳定性、能量泛函和卡勒-爱因斯坦度量
DOI：
10.4310/cag.2003.v11.n3.a6
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发表时间：
2002
影响因子：
0.7
通讯作者：
J. Sturm
中科院分区：
文献类型：
--
作者：
D. Phong;J. Sturm
一个明确的警告$||F||在射影簇的Chow向量的向量空间上引入了_{#}$，并证明了它是Chow簇的一个广义Mabuchi能量泛函.的奇异性的周品种产生的电流支持其奇异轨迹，而经常性的部分，再现相应的投影品种的马渊能量泛函。因此，Mabuchi泛函的下有界性，以及K\“ahler-Einstein度量的存在性，与当前$[Y_s]$和当前$的行为有关。||F||_{#}$沿着SL（N+1，{\bf C}）$的轨道。
An explicit seminorm $||f||_{#}$ on the vector space of Chow vectors of projective varieties is introduced, and shown to be a generalized Mabuchi energy functional for Chow varieties. The singularities of the Chow varieties give rise to currents supported on their singular loci, while the regular parts are shown to reproduce the Mabuchi energy functional of the corresponding projective variety. Thus the boundedness from below of the Mabuchi functional, and hence the existence of K\"ahler-Einstein metrics, is related to the behavior of the current $[Y_s]$ and the seminorm $||f||_{#}$ along the orbits of $SL(N+1,{\bf C})$.